Chapter 8: Q. 31 (page 755)

In the following exercises, simplify using absolute values as necessary.
$ⓐ \sqrt[]{x^{6}} ⓑ \sqrt[]{y^{16}}$

Short Answer

Expert verified

Part(a) $\sqrt[]{x^{6}} = |x|$

Part(b) $\sqrt[]{y^{16}} = y^{8}$

Step by step solution

Part(a) Step 1. Given information

$ⓐ \sqrt[]{x^{6}}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l} Since {(a^{m})}^{2} = a^{2 m} \\ \to {(x^{3})}^{2} = x^{2 * 3} \\ \to {(x^{3})}^{2} = x^{6} \\ Sincetheindexniseven, \sqrt[n]{a^{n}} = |a| . \\ Herenisanevennumber \\ \sqrt[]{x^{6}} = |x| \end{array}$

Part(b) Given information

$ⓑ \sqrt[]{y^{16}}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l} \begin{array}{l} Since {(a^{m})}^{2} = a^{2 m} \\ \to {(y^{8})}^{2} = y^{2 * 3} \\ \to {(y^{8})}^{2} = y^{16} \\ Sincetheindexniseven, \sqrt[n]{a^{n}} = |a| . \\ Herenisanevennumber \\ \sqrt[]{y^{16}} = |y| \\ {Inthiscasetheabsolutevaluesignisnotneededasy}^{8} ispositive. \\ \sqrt[]{y^{16}} = y^{8} \end{array} \end{array}$

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In the following exercises, simplify using absolute values as necessary.
$ⓐ \sqrt[]{x^{6}} ⓑ \sqrt[]{y^{16}}$

Short Answer

Step by step solution

Part(a) Step 1. Given information

Step 2. Explanation

Part(b) Given information

Step 2. Explanation

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In the following exercises, simplify using absolute values as necessary.ⓐx6ⓑy16

Short Answer

Step by step solution

Part(a) Step 1. Given information

Step 2. Explanation

Part(b) Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

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Pure Maths

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute values as necessary.
$ⓐ \sqrt[]{x^{6}} ⓑ \sqrt[]{y^{16}}$